Answer
See below
Work Step by Step
Given that the two expressions, $f(x)$ and $g(x)$, are functions, we know that they will follow the rules of functions listed on page 429. Knowing this, we obtain:
$$f(x)-g(x)=-3x^{1/3}+4x^{1/2}-(5x^{1/3}+4x^{1/2}\\=(-3x^{1/3}-5x^{1/3})+(4x^{1/2}-4x^{1/2})\\=- 8x^{1/3}$$
$f(x)$ and $g(x)$ have the same domain: all nonnegative real numbers. Hence, the domain of $f(x)-g(x)$ is the same: all nonnegative real numbers.
